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Graham

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  • Richard DeemingR Offline
    Richard DeemingR Offline
    Richard Deeming
    wrote on last edited by
    #1

    Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


    "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

    "These people looked deep within my soul and assigned me a number based on the order in which I joined" - Homer

    R S L D M 8 Replies Last reply
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    • Richard DeemingR Richard Deeming

      Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


      "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

      R Offline
      R Offline
      racketeer
      wrote on last edited by
      #2

      Couldn't you wait your turn? :)

      Richard DeemingR 1 Reply Last reply
      0
      • R racketeer

        Couldn't you wait your turn? :)

        Richard DeemingR Offline
        Richard DeemingR Offline
        Richard Deeming
        wrote on last edited by
        #3

        :laugh:


        "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

        "These people looked deep within my soul and assigned me a number based on the order in which I joined" - Homer

        1 Reply Last reply
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        • Richard DeemingR Richard Deeming

          Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


          "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

          S Offline
          S Offline
          Simon_Whale
          wrote on last edited by
          #4

          Now you've made my head hurt I'm going home!

          Every day, thousands of innocent plants are killed by vegetarians. Help end the violence EAT BACON

          1 Reply Last reply
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          • Richard DeemingR Richard Deeming

            Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


            "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

            L Offline
            L Offline
            Lost User
            wrote on last edited by
            #5

            Richard Deeming wrote:

            Because all smaller numbers are irrelevant. ;-P

            Still a finite number :rolleyes:

            Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^]

            Richard DeemingR 1 Reply Last reply
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            • L Lost User

              Richard Deeming wrote:

              Because all smaller numbers are irrelevant. ;-P

              Still a finite number :rolleyes:

              Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^]

              Richard DeemingR Offline
              Richard DeemingR Offline
              Richard Deeming
              wrote on last edited by
              #6

              Indeed, and so much more interesting than ∞. :)


              "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

              "These people looked deep within my soul and assigned me a number based on the order in which I joined" - Homer

              D 1 Reply Last reply
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              • Richard DeemingR Richard Deeming

                Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


                "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                D Offline
                D Offline
                Daniel Pfeffer
                wrote on last edited by
                #7

                The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4),[*] are extremely small by comparison.[1] A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of As is A(187196),[2] and A() is a version of Ackermann's function: A(x) = 2 [x + 1] x in hyperoperation. Graham's number, for example, is approximately A^64(4) which is much smaller than the lower bound A^A(187196)(1). http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#Friedman.27s_finite_form[^] I think it's time that we all went home...

                If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                Richard DeemingR K 2 Replies Last reply
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                • Richard DeemingR Richard Deeming

                  Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


                  "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                  M Offline
                  M Offline
                  Mark_Wallace
                  wrote on last edited by
                  #8

                  That's crackers.

                  I wanna be a eunuchs developer! Pass me a bread knife!

                  1 Reply Last reply
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                  • Richard DeemingR Richard Deeming

                    Indeed, and so much more interesting than ∞. :)


                    "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                    D Offline
                    D Offline
                    Daniel Pfeffer
                    wrote on last edited by
                    #9

                    All natural integers are interesting. (The proof is left as an exercise for the student)

                    If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                    1 Reply Last reply
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                    • D Daniel Pfeffer

                      The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4),[*] are extremely small by comparison.[1] A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of As is A(187196),[2] and A() is a version of Ackermann's function: A(x) = 2 [x + 1] x in hyperoperation. Graham's number, for example, is approximately A^64(4) which is much smaller than the lower bound A^A(187196)(1). http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#Friedman.27s_finite_form[^] I think it's time that we all went home...

                      If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                      Richard DeemingR Offline
                      Richard DeemingR Offline
                      Richard Deeming
                      wrote on last edited by
                      #10

                      Daniel Pfeffer wrote:

                      I think it's time that we all went home...

                      Apart from those of us who work from home, who should all go down the pub. :rolleyes:


                      "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                      "These people looked deep within my soul and assigned me a number based on the order in which I joined" - Homer

                      D 1 Reply Last reply
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                      • Richard DeemingR Richard Deeming

                        Daniel Pfeffer wrote:

                        I think it's time that we all went home...

                        Apart from those of us who work from home, who should all go down the pub. :rolleyes:


                        "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                        D Offline
                        D Offline
                        Daniel Pfeffer
                        wrote on last edited by
                        #11

                        :thumbsup::thumbsup::thumbsup:

                        If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                        1 Reply Last reply
                        0
                        • Richard DeemingR Richard Deeming

                          Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


                          "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                          C Offline
                          C Offline
                          Corporal Agarn
                          wrote on last edited by
                          #12

                          So the U.S. debt is trying to surpass Graham's number?

                          Mongo: Mongo only pawn... in game of life.

                          1 Reply Last reply
                          0
                          • Richard DeemingR Richard Deeming

                            Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


                            "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                            G Offline
                            G Offline
                            Gary Wheeler
                            wrote on last edited by
                            #13

                            Any mathematicians in the crowd are watching the children play with matches.

                            Software Zen: delete this;

                            D 1 Reply Last reply
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                            • D Daniel Pfeffer

                              The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4),[*] are extremely small by comparison.[1] A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of As is A(187196),[2] and A() is a version of Ackermann's function: A(x) = 2 [x + 1] x in hyperoperation. Graham's number, for example, is approximately A^64(4) which is much smaller than the lower bound A^A(187196)(1). http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#Friedman.27s_finite_form[^] I think it's time that we all went home...

                              If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                              K Offline
                              K Offline
                              kmoorevs
                              wrote on last edited by
                              #14

                              Can you spell that sequence using only A, C, G, and T? :laugh:

                              "Go forth into the source" - Neal Morse

                              D 1 Reply Last reply
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                              • K kmoorevs

                                Can you spell that sequence using only A, C, G, and T? :laugh:

                                "Go forth into the source" - Neal Morse

                                D Offline
                                D Offline
                                Daniel Pfeffer
                                wrote on last edited by
                                #15

                                Yes, but the representation is too large to fit in the margins of Code Project :)

                                If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                                R 1 Reply Last reply
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                                • G Gary Wheeler

                                  Any mathematicians in the crowd are watching the children play with matches.

                                  Software Zen: delete this;

                                  D Offline
                                  D Offline
                                  Daniel Pfeffer
                                  wrote on last edited by
                                  #16

                                  Gary Wheeler wrote:

                                  Any mathematicians in the crowd are watching the children play with matches.

                                  For my next act, I will wrassle a bear, make peace with a feral Chtorran, and divide by zero! [Bonus points for identifying the references]

                                  If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                                  E 1 Reply Last reply
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                                  • D Daniel Pfeffer

                                    Gary Wheeler wrote:

                                    Any mathematicians in the crowd are watching the children play with matches.

                                    For my next act, I will wrassle a bear, make peace with a feral Chtorran, and divide by zero! [Bonus points for identifying the references]

                                    If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                                    E Offline
                                    E Offline
                                    eshill
                                    wrote on last edited by
                                    #17

                                    "Then for my first encore, I drink a whole bottle of trans-Lunar brandy, make love to a feral Chtorran, and kill a Martian woman-I think. Or maybe it's the other way around." David Gerrold in The Voyage of the Star Wolf. :)

                                    D 1 Reply Last reply
                                    0
                                    • Richard DeemingR Richard Deeming

                                      Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


                                      "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                                      M Offline
                                      M Offline
                                      Matthew Dennis
                                      wrote on last edited by
                                      #18

                                      I think this is how mathematicians and astrophysists play "Mine's bigger than yours" :laugh:

                                      1 Reply Last reply
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                                      • E eshill

                                        "Then for my first encore, I drink a whole bottle of trans-Lunar brandy, make love to a feral Chtorran, and kill a Martian woman-I think. Or maybe it's the other way around." David Gerrold in The Voyage of the Star Wolf. :)

                                        D Offline
                                        D Offline
                                        Daniel Pfeffer
                                        wrote on last edited by
                                        #19

                                        Correct!

                                        If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                                        1 Reply Last reply
                                        0
                                        • D Daniel Pfeffer

                                          Yes, but the representation is too large to fit in the margins of Code Project :)

                                          If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                                          R Offline
                                          R Offline
                                          racketeer
                                          wrote on last edited by
                                          #20

                                          :laugh:

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